As mentioned earlier, a central notion in SI is the so-called pairwise influence matrix \({{\mathcal {I}}}^{\Lambda ,\tau }_{G}\) .
Given a set of parameters of the Gibbs distribution, the endeavour is to show that the maximum eigenvalue of
\({{\mathcal {I}}}^{\Lambda ,\tau }_{G}\)  is \(O(1)\) .
Previously introduced approaches in [1]}, [2]} have been focusing on proving that
either \(|| {{\mathcal {I}}}^{\Lambda ,\tau }_{G} ||_1\) , or \(|| {{\mathcal {I}}}^{\Lambda ,\tau }_{G} ||_{\infty }\)  is bounded, which
in turn implies that the maximum eigenvalue is bounded.
These approaches are quite elegant and provide, in a very natural way, bounds that depend on the maximum
degree \({\Delta }\) . However, for our purposes here they seem to be too crude.
